Structural changes during phase transitions and the critical and noncritical order parameters in the (NH₄)₃Nb(O₂)₂F₄ crystal

Abstract

The structures of two phases of the (NH₄)₃Nb(O₂)₂F₄ crystal, namely, the parent cubic phase and the most distorted low-temperature phase, have been determined from data of an X-ray diffraction experiment performed for a powder sample. The profile and structural parameters have been refined according to the procedure implemented in the DDM program. The results obtained have been discussed with invoking the group-theoretical analysis of the complete order parameter condensate, which takes into account the critical and noncritical atomic displacements and allows the interpretation of the obtained experimental data. It has been found that the most probable sequence of structural transformations occurring in the crystal can be schematically represented in the following form:

$$\begin{gathered} Fm\bar 3m\xrightarrow[{(\eta 1,\eta 1,\eta )}]{{\Gamma _5^ + (11 - 7)}}C2/m\xrightarrow[{(\eta 1,\eta 1,\eta )(0,0,0,0,0,\xi ,0 - \xi ,0,0,0,0)}]{{\Gamma _5^ + (11 - 7) \otimes \Sigma _2 (4 - 2)}}P2_1 /m \hfill \\ \xrightarrow[{(\eta 1,\eta 1,\eta )(0,0,0,0,0,\xi ,0 - \xi ,0,0,0,0)(0,0,0,0,0,\varepsilon ,0,\varepsilon ,0,0,0,0)}]{{\Gamma _5^ + (11 - 7) \otimes \Sigma _2 (4 - 2) \otimes \Sigma _3 (4 - 3)}}P2_1 /n. \hfill \\ \end{gathered} $$